Momentum

•A measure of how hard it is to stop a moving object.

•Related to both mass and velocity.

•Possessed by all moving objects.

Calculating Momentum

•For one particlep = mv

•For a system of multiple particlesP = pi = mivi

•Momentum is a vector!

Which has the most momentum?

Impulse (J)

The product of an external force and time, which results in a change in momentum•J = F t•J = P•Units: N s or kg m/s

Impulse (J)F(N)

t (ms)0 1 2 3 40

1000

2000

3000

area under curve

Law of Conservation of Momentum

If the resultant external force on a system is zero, then the vector sum of the momenta of the objects will remain constant.

ppbb == ppaa

Collisions• Collisions are governed by

Newton's laws. • Newton’s Third Law tells us that

the force exerted by body A on body B in a collision is equal and opposite to the force exerted on body B by body A.

Collisions

During a collision, external forces are ignored. The time frame of the collision is very short.The forces are impulsive forces (high force, short duration).

Collision Types• Elastic (hard, no deformation)

– P is conserved, K is conserved

• Inelastic (soft; deformation)– P is conserved, K is NOT conserved

• Perfectly Inelastic (stick together)– P is conserved, K is NOT conserved

Golf and Momentum

Consider the elastic collision between the club head and the golf ball in the sport of golf.

Golf and Momentum

Forces are on the clubhead and ball are equal and opposite.

Golf and Momentum

The acceleration of the ball is greater because its mass is smaller.

Pool and Momentum

Consider the elastic collision between a moving ball and a ball that is at rest in the sport of billiards.

Pool and Momentum

The balls experience forces which are equal in magnitude and opposite in direction.

Pool and Momentum

Since the balls have equal masses, they experience equal accelerations.

Explosion• When an object separates suddenly, this

is the reverse of a perfectly inelastic collision.

• Mathematically, it is handled just like an ordinary inelastic collision.

• Momentum is conserved, kinetic energy is not.

• Examples:– Cannons, Guns, Explosions, Radioactive

decay.

Perfectly Inelastic Collision #1

An 80 kg roller skating grandma collides inelastically with a 40 kg kid as shown. What is their velocity after the collision?

Perfectly Inelastic Collisions #2

A train of mass 4m moving 5 km/hr couples with a flatcar of mass m at rest. What is the velocity of the cars after they couple?

Perfectly Inelastic Collisions #3

A fish moving at 2 m/s swallows a stationary fish which is 1/3 its mass. What is the velocity of the big fish and after dinner?

Recoil Problem #1

A gun recoils when it is fired. The recoil is the result of action-reaction force pairs. As the gases from the gunpowder explosion expand, the gun pushes the bullet forwards and the bullet pushes the gun backwards.

Sample Problem

Suppose three equally strong, equally massive astronauts decide to play a game as follows: The first astronaut throws the second astronaut towards the third astronaut and the game begins. Describe the motion of the astronauts as the game proceeds. Assume each toss results from the same-sized "push." How long will the game last?

Announcements 04/18/23

• Tomorrow -- Graded Quiz• Lunch Bunch Wednesday this week!• Lunch Bunch HW due Wednesday.• Exam Thursday on Momentum.• Energy Exam corrections M,Tue,Thu• Makeup lab on Friday.

Center of Mass• Physicist like to deal with particles

because it is relatively easy to deal with an object that has position and mass, but no real size.

• But what do you do if you have a real object with a non-zero size? Or if you have a collection of particles?

• You turn the object into a particle by pretending all the mass resides at the center of mass.

Calculate momentum of the balls before and after the collision.

3 m/s

2 kg 8 kg

0 m/s

Before

2 m/s2 kg

8 kgV?

After

50o

Center of Mass

The point at which all of the mass of an object or system may be considered to be concentrated.

Center of Mass for solid objects

Pick the geometric center of the object

x

x x

Center of Mass for collection of points

xcm = mixi / M

ycm= miyi / M

zcm= mizi / M

Center of Mass Problem (SOS 8.10)A system consists of the following masses in the x,y plane: 4 kg at (0, 5m), 7 kg at (3m, 8m), and 5 kg at (-3 m, -6m). Find the position of its center of mass.